Highest densities of mountain hares (Lepus timidus) associated with ecologically restored bog but not grouse moorland management

Abstract Over the last 20 years, ecological restoration of degraded habitats has become common in conservation practice. Mountain hares (Lepus timidus scoticus) were surveyed during 2017–2021 using 830 km of line transects in the Peak District National Park, England. Historically degraded bog areas were previously reported having low hare numbers. Following bog restoration, we found hare densities of 32.6 individuals km−2, notably higher than neighboring degraded (unrestored) bog with 24.4 hares km−2. Hare density on restored peatland was 2.7 times higher than on bogs managed for grouse shooting at 12.2 hares km−2 and 3.3 times higher than on heather moorland managed for grouse shooting at 10.0 hares km−2. Yearly estimates varied most on habitats managed for grouse, perhaps indicative of the impact of habitat management, for example, heather burning and/or possible hare culling to control potential tick‐borne louping ill virus in gamebirds. Acid grassland used for sheep farming had a similar density to grouse moorland at 11.8 hares km−2. Unmanaged dwarf shrub heath had the lowest density at 4.8 hares km−2. Hare populations are characterized by significant yearly fluctuations, those in the study area increasing by 60% between 2017 and 2018 before declining by ca. 15% by 2020 and remaining stable to 2021. During an earlier survey in 2002, total abundance throughout the Peak District National Park was estimated at 3361 (95% CI: 2431–4612) hares. The present study estimated 3562 (2291–5624) hares suggesting a stable population over the last two decades despite fluctuations likely influenced by weather and anthropogenic factors. Mountain hares in the Peak District favored bog habitats and were associated with restored peatland habitat. Wildlife management should be cognizant of hare density variation between habitats, which may have implications for local extinction risk.


| INTRODUC TI ON
Across the world, many ecosystems are suffering anthropogenic damage with wide-ranging impacts (IPBES, 2019). Among these are peatlands, wetland ecosystems where decomposing vegetation has taken thousands of years to accumulate as peat layers. These are often vulnerable to human activities (e.g., cutting, grazing, burning, and indirect erosion) and sensitive; their replacement may require millennia (Page & Baird, 2016;Yu et al., 2016). In the northern hemisphere, peatlands experience cold-wet climates, providing the conditions for peat layer development. Peatland habitat stores approximately 50% of total global soil carbon storage (Evans et al., 2006), while hosting environmentally sensitive plants and animals of high conservation importance. Across Europe, many peatlands are degraded (Urak et al., 2017) and substantial funds (e.g., ~ €167 m in EU Life projects) have been invested in peatland restoration in recent decades, recognizing its importance for carbon sequestration, water retention, and biodiversity (Andersen et al., 2017).
The South Pennine Moors contains 650 km 2 of UK upland peatland distribution (Bonn et al., 2009;JNCC, 2015) and received Special Areas of Conservation (SAC) designation in 2005 for its unique upland plant community and population of breeding waders (Natural England, 2005. This area features peatlands which have suffered extensive human-caused degradation (Evans, 2009).
Over the last two centuries, atmospheric pollutant deposition from the surrounding industrial cities including Sheffield and Manchester led to local soil acidification and loss of sphagnum, severely harming vegetation, leaving bare peat and extensive gully erosion (Alderson et al., 2019;Andersen et al., 2017;Natural England, 1993;Tallis, 1997Tallis, , 1998. Within the SAC are ~350 km 2 of grouse moor estates practicing rotational heather burning and predator management, creating an ecosystem supporting red grouse (Lagopus lagopus) for shooting (Phillips, 2012;Sotherton, 2009). There are also areas, which have seen extensive sheep (Ovis aries) overgrazing, where former upland dry heath has transitioned to acid grassland (Anderson & Yalden, 1981). The frequency of accidental or deliberate wildfires has also increased (McMorrow et al., 2009). All these anthropogenic mechanisms have been implicated in causing extensive moorland degradation, precipitating much loss of diversity of flora and fauna (Anderson & Shimwell, 1981;Pearce-Higgins et al., 2006;Sim et al., 2005;Tallis, 1998;Thompson et al., 1995;Tucker, 2003). Recent evaluation of habitat conditions for the South Pennine Moors SAC rated the area as 99% "unfavorable-recovering" or "unfavorable-no change" (Natural England, 2021).  (Alderson et al., 2019;Bedson in litteris.). Conservation measures included fencing out grazing animals, reduced burning and trampling, and removal of species, for example, Molinia. Hydrology was re-established with gully blocking. Bare peat was restored with netting, fertilizers, liming, mulches and reseeding and replanting with grasses, rushes, mosses, dwarf shrubs, heather, and eventually Sphagnum moss (Alderson et al., 2019;Buckler et al., 2013). Many bare peat areas recovered their vegetation (Alderson et al., 2019). However, little was known about the effects on wildlife (Andersen et al., 2017;Shepherd et al., 2013).
The mammal species mountain hare (Lepus timidus scoticus) has been regarded as a useful habitat quality indicator (JNCC, 2008).
In England, mountain hares became extinct around 6000 bp and were reintroduced to areas of the South Pennines Moors lying within the present-day Peak District National Park, by landowners with sporting interests in the 1870s (Harris & Yalden, 2008). From the 1970s, studies described a small, stable population of ~1000 individuals (Mallon, 2001;Yalden, 1971Yalden, , 1984. The last field study estimated ~10,000 individuals, inconsistent with previous research (Mallon et al., 2003). The most recent estimate was 2500 individuals (Mathews et al., 2018). Mountain hares were associated with mixed Calluna/Eriophorum areas or Calluna areas on grouse moors (Mallon et al., 2003;Yalden, 1971), and there were concerns about the persistence of these habitats (JNCC, 2007).
The aim of this research was to estimate mountain hare densities in different upland habitats. We surveyed mountain hares over 5 years and evaluated evidence whether habitat restoration and/or grouse moor management was concomitant with high hare population density. In 1 year, we also surveyed the whole National Park to report overall mountain hare abundance. This research was intended to accomplish investigations recommended by the UK Biodiversity Action Plan (JNCC, 2008) and to inform future conservation status assessments.

| Study area
Fieldwork was conducted on upland habitats in the Peak District National Park, lying within the South Pennine Moors SAC ( Figure 1). These uplands are underlain by acidic gritstone and shale rocks forming hills up to ~630 m. The annual average temperature is 10.3°C and precipitation 1025 mm, creating a wet substrate on hill tops (UK Met Office, 2020). The hills are covered with peat, up to 2 m deep (Anderson & Shimwell, 1981). The study extent was informed by UK Biological Record Centre (BRC) mountain hare observations (See Acknowledgments) for the period 1998-2018, eliciting 8666 records. From these, we mapped a minimum convex polygon 610 km 2 constituting the observed mountain hare range in our study area ( Figure 1).

| Habitat classes
We developed a habitat classification map by layering several data sources and mapping with a 1-ha scale cell grid (i.e., 100 cells km −2 ) in ArcGIS (ESRI USA) ( Figure 2). Habitat classes pertaining to mountain hare occupancy were acid grassland, upland dwarf shrub heath, and wet upland blanket bog (Jackson, 2000;Natural England, 2005, with extent informed by the UK landcover map (Rowland et al., 2017). Other habitats had very few mountain hare records and were deemed irrelevant.
To identify grouse moor areas, we followed methods from Yallop et al. (2006) and assembled a mosaic of 1:500 scale aerial images dated for 2018 (Digimap, 2019). Any 1-ha cell showing a burn or mowed patch was designated as "grouse moor bog" or "grouse moor heather" depending on underlying landcover (Rowland et al., 2017).
The remaining heather area not grouse moor was classified as "unmanaged dwarf shrub heath" at elevations 250-520 m including steep slopes and few gullies. This comprised mosaics of 70% dense/30% open heather, predominantly Calluna (Rowland et al., 2017), height to 120 cm (Bardgett et al., 1995;Stace, 2010). There was no predator control and few sheep.
We identified "restored bog" from shapefiles provided by the conservation partnership "Moors for the Future" (Acknowledgments), designating their recovery work to 2016. These areas measured ~20 km 2 , occurring at elevations 480-630 m and comprised previously degraded bare peat. From 2007, restoration efforts included gully blocking, fertilizer, liming, laying of jute textiles, reseeding, planting, and spreading heather brash (Alderson et al., 2019). By 2016, this work achieved 75% vegetation cover (Alderson et al., 2019); much was in lush, verdant condition. Vegetation comprised a wide variety of moorland species, which shifted frequently in composition over the space of a few meters, including Calluna, Eriophorum, and Sphagnum spp., shrubs (e.g., Erica tetralix, E. cinerea, Rubus chamaemorus, Vaccinium mytrillus, and Empetrum nigrum), ferns (e.g., Oreopteris limbosperma and Blechnum spicant), herbs (e.g., Potentilla erecta, Viola F I G U R E 1 Map of study area. The locations of 10 years of BRC mountain hare records informed the minimum convex polygon, being the outer shape. The extent of hares for abundance projection was the alpha hull shape, shown by the blue line and also the survey areas. The survey transects are shown for Bleaklow and Margery Hill (black squares); Holme Moss (red squares); and peripheral areas (dotted squares). Legend shows habitat classes. Inset map shows location of Peak District in the United Kingdom. Peak District map origin is British National Grid Reference SK Easting 390000 Northing 370000. North at top palustris, Chamerion angustifolium, and Galium saxatile), and mosses (e.g., Hypnum jutlandicum and Polytrichum spp). Calluna height was up to ~100 cm; winter grasses were senescent reaching heights ~30 cm (Stace, 2010). The extensive networks of eroded gullies were revegetated, and the water table was high (Alderson et al., 2019). There was no predator control practiced, and sheep were fenced out.
The remaining bog areas were classed as "unrestored bog" at elevations 300-630 m. These had not historically deteriorated to the point of comprising bare peat, yet nonetheless appeared ecologically impoverished, that is, "unfavorable-recovering" condition (Natural England, 2019). They consisted mostly of extensive fields of Eriophorum spp. and Molinia caerulea grass, winter height ~30 cm, and some Calluna patches height ~100 cm (Stace, 2010) with lower species diversity than restored bog areas. They featured eroded gullies, without gully blocking as was the case for "restored bog," therefore drier with water run-off. No predator control was practiced, and there were some sheep.
Ground and aerial photographs showing habitat classes appear in Figure 3. Table 1 lists vegetation communities. Habitat class data for hare observations, transect lengths, and surveyed area size were then determined using "extract" function in package Raster (Hijmans & van Etten, 2012) within R (R Core Team, 2021).

| Surveys
When planning surveys, we perceived a random stratified approach (Morrison et al., 2010) might miss local concentrations of mountain hares (Flux, 1962) with typical small home ranges from ~10 ha (Rao et al., 2003) to ~100 ha (Hewson & Hinge, 1990). We, therefore, designated survey sites as 5 × 5 km, potentially identifying hare density patterns over a few hundred meters and large enough to encompass all habitat classes. During pilot surveys, we observed mountain hares up to 700 m range and so conducted transects in sampled 1 km squares of the Ordnance Survey grid (OS Explorer Map1, 2015), achieving continuous coverage probability >.01. The perimeter of each square was surveyed as a circuit, walking all four sides as one continual transect. By walking all cardinal directions, we intended this to account for sampling differences arising from slope, weather, or lighting. We considered each 1-km transect to be independent. At adjoining corners of squares, there was overlap of visual coverage (at a subsequently modeled range 520 m), meaning corners were surveyed twice a year compared with remaining areas surveyed once. We assessed this coverage (Table A1) using Pearson's chi-square test, which reported no significant difference in proportion of habitat classes surveyed twice, versus once: χ 2 (5) = 3.588, p = .61. Hence, we did not modify estimates for differing coverage probabilities. Therefore, we met standard distance sampling assumptions with survey effort acting as denominator for encounter rate (Buckland et al., 2001, 233-235;Buckland et al., 2004, 224;Buckland et al., 2015, 27).
To meet our aim of surveying the entire mountain hare population at our sites, our study sampling was designed to make efficient use of limited staff time and good weather days. From BRC records, we noted 37% of historic observations were on 23% of the study area: Bleaklow and Margery Hill, with 4 km of non-surveyed land between them ( Figure 1). Thus, we configured the 5 × 5 km sites atop these two hills, acknowledging that ensuing density estimates might be higher than elsewhere in the wider park. We surveyed alternate 1 km 2 squares, that is, 13 squares on Bleaklow, 13 squares on Mountain hare observations were made using standard distance sampling methods, recording date, time, grid reference, cluster size, distance to hare (Nikon ProStaff7i laser range finder, accuracy 1m), and angle (compass and angle board) (Buckland et al., 2001).
Potential double counts for observation were discounted. Previous studies described difficulties of daytime surveys for mountain hares, as this nocturnal species often hides by day, revealing itself by flushing from cover, a difficulty associated with tall heather on grouse moor habitats, contributing to imprecise density estimates (Bedson, Thomas, et al., 2021;Newey et al., 2003Newey et al., , 2018 To evaluate whether this behavior affected the detection process, we categorized hare activity upon first being observed, as stationary (lying or sat up); moving (walking, running, or feeding); or flushing (emerging from cover). Surveys were conducted under similar conditions for comparable previous studies in clear weather with wind speed <20 mph (e.g., Newey et al., 2018). We assumed stronger winds did not influence hare detections (e.g., Flux, 1962), but caused difficulties holding the laser range finder steady. No surveys were conducted with snow present.

| Distance modeling
For Bleaklow and Margery Hill, mountain hare observations were attributed to the habitat class on which the animal was first seen (as represented in Figure 1). To consider the possibility of field

F I G U R E 2
Step-by-step construction of habitat class map for surveyed extent (5 × 5 km with 800 m buffer) with 1-ha pixel, for each of Bleaklow (left) and Margery Hill (right) (British National Grid origin SK Easting 408000 Northing 394000). Map (a) shows landcover classification system of Rowland et al. (2017), which is used as starting point. Map (b) Aerial photographs are assessed and any with burn mark within any hectare denoted as either grouse moor bog or grouse heather, referencing the underlying landcover determined by Rowland et al. (2017). Map (c) Shapefiles provided by Moors for the Future, showing recovering bog areas which received treatment up to 2016. Map (d) The final map with all habitat classes pertinent to mountain hares. Any heather without burn mark is, therefore, regarded as unmanaged dwarf shrub heath measurement errors (GPS, laser range finder, and angle board) affecting habitat class assignment, within ArcGIS we applied buffers of 25 m circles to all observations and found 97.3% of these lay wholly within the observation's extracted habitat class; 2.7% straddled two habitat classes. We accepted this as tolerable systematic error. We excluded Holme Moss and peripheral areas from habitat analyses as they were not surveyed every year, retaining them for discrete "area only" estimations.
We analyzed our data with DISTANCE v.7.3 (Thomas et al., 2010), using different data filtering and model selections. We assessed different truncation distances and bin widths. We compared detection models with three key functions: uniform, half-normal, and hazard rate, with cosine or polynomial expansion terms (Buckland et al., 2001, 47;Williams & Thomas, 2007). We assessed the suitability of assumptions and models using histograms, quantile-quantile plots, χ 2 goodness of fit statistics, and the fit of the detection function close to the transect line g(0). We compared and sought simple models with few parameters, lower AIC values between models using the same data selection, higher χ 2 goodness of fit statistics, and lower detection probability cv values (Buckland et al., 2001). The furthest observation distance was 780 m. We truncated the data at a range of 520 m. The hazard-rate model provided its characteristic wide shoulder and steep drop off of the detection function with increasing perpendicular distance. With data truncated at 520 m, this provided a high χ 2 goodness of fit statistic (0.77) for the detection function, with p = .18 and low detection probability cv = 0.04 (Table   A2, Figure 4). Both the uniform and half-normal models failed to achieve a suitable (i.e., >0.05) χ 2 goodness of fit statistic with most data selections.
We compared two approaches to stratification by habitat: (1) global detection function using pooled data, this required three parameters, reporting AIC 22,148.43, global P cv = .04; (2) strata F I G U R E 3 Photographs of each of the habitat classes. For each habitat class, the left field photograph is taken from the ground. The right side photographs are aerial images at 300 m by 300 m with a 100 m fishnet grid overlain, for scale. Source: ArcGIS ESRI "WorldImagery" downloaded 3 August 2021. Colors are natural, not enhanced. Note each field photograph also contains an example mountain hare observation (i.e., habitat class)-specific detection function, this required 16 parameters, reporting AIC = 22,110.73, ∆AIC = 37.70 ( Figure 4). The lower AIC of the strata-specific detection function indicated this model was best. However, for some habitats this estimated high P cv values: acid grassland = .24; grouse moor heather = .30; and unmanaged dwarf shrub heath = .36, leading to greater uncertainty for density estimates. Additionally, the detection function for unrestored bog was invalid (g(0) > 1) and the sample size for unmanaged dwarf shrub heath was 37 observations, below that recommended by Buckland et al. (2001), exacerbating doubts about estimate validity. Meanwhile, attempts to use strata as covariates resulted in greater AIC values and were dismissed.
We considered how the strata-specific detection function var- We assessed whether hare detectability (hiding behavior) varied between habitat classes. For all observations, hare activity was recorded as 61% stationary, 21% moving, and 19% flushing from TA B L E 1 Ecosystems and habitat classes used in this research and the plant communities within these areas, as described by the British National Vegetation Classification (NVC) (Elkington et al., 2001;Hall et al., 2004;Jackson, 2000;JNCC, 2015;Natural England, 2005;Rowland et al., 2017) F I G U R E 4 Histograms for Bleaklow and Margery Hill distance sampling data from 2017 to 2021 (1985 observations) fitted with the hazard-rate model truncated at 520 m. The first histogram shows all data, pooled, as used for reporting. The subsequent six histograms show detection functions when stratified by habitat class with parameters: n = sample size; χ 2 GOF (p) = chi-square goodness of fit p-value; P = detection probability P cv = coefficient of variation; ESW = effective strip width in meters. Detection function for unrestored bog reports detection probability at the transect line >1, that is, invalid model. The column charts bottom right show detection probability and effective strip width estimates with 95% confidence intervals. All = from global detection function all data, pooled, showing much narrower confidence intervals than the subsequent six columns where the detection function is stratified by habitat class cover, varying per habitat class and radial distance. To test for relationships between these factors, we calculated encounter rate, allocating untruncated observations to 18 radial distance bin widths of ~43 m ( Figure A1), that is, resembling habitat stratified detection function histograms (Figure 4). Some activities were not observed at certain ranges, so log-linear analysis was not possible (Field et al., 2012, 837). Therefore, we grouped observations as within or be-  (Buckland et al., 2001, 89-91).
We stratified the sampling data and reported in four ways: (1) by habitat class, that is, pooling all observations in each habitat class over the 5 years together; (2) by year, that is, pooling all observations in each year, without habitat information; (3) by habitat and by each year, that is, 6 habitats × 5 years = 30 strata; and (4) by area only and to enable the 2019 population estimate. This was accomplished within software distance, using the same data, each time allocating transects and observations to different strata definitions (Thomas et al., 2010). Estimates for the survey year 2019 also used data truncated at 520 m and the hazard-rate model; inevitably its global detection function f(0) differed slightly from the smaller data set of Bleaklow and Margery Hill. We reported parameters and estimates with 95% confidence intervals. Comparisons between strata used the t-statistic based on the Satterthwaite approximation, accounting for unequal sample sizes (Buckland et al., 2001, 84-86). This test takes into account the lack of independence of data arising from using a common detection function between strata. We evaluated significance with a Bonferroni-corrected p-value and also calculated effect sizes (Field et al., 2012).
Abundance for the Peak District National Park was calculated for 2019 based on the additional survey effort. The 2019 survey showed very strong density fall off from center to edge of the Park.
Therefore, to determine the extent for calculating abundance, we created an alpha hull shape measuring 325 km 2 , from BRC hare records ( Figure 1). We discarded six outlying records to cover only the known range of hares. This alpha hull shape differed very slightly from our survey area, so we merged them based on habitat classes to total 358 km 2 . Abundance was calculated for each of Bleaklow  Figure A2). Cluster sizes were slightly above 1.0; most encounters were single hares (Table 2, Table A3, Figure A2).  Figure A3).

| Density and abundance
On  Table 2, Figures 5 and 6). There were significant differences for 10 paired comparisons of habitats (Table A4).
Hare densities on restored bog were significantly higher (p < .05) than all other habitats except unrestored bog; densities in the former were 34% higher than the latter: t(1.92) = 99.03, p = .057, r = .19.
Unrestored bog also showed significantly higher densities than the other classes. Acid grassland, grouse moor heather, and grouse moor bog were similar. Grouse moor bog hare density was not significantly higher than grouse moor heather t(0.76) = 47.19, p = .449, r = .11. Acid grassland and grouse moor bog were significantly higher than unmanaged dwarf shrub heath. Grouse moor heather was higher than unmanaged dwarf shrub heath t(1.90) = 43.10, p = .064, r = .28. When comparing habitats within each individual year, many of these differences were often apparent in individual years (Tables A3 and A5). Of the 2019 survey areas, the highest density of hares was reported for Bleaklow with 27.2 hares km −2 (95% CI: 19.9-37.9), significantly higher than any other area (Tables 2 and A4, Figure A4).

| DISCUSS ION
We report strong evidence that mountain hare density differs between peatland habitat types. We found intensely localized hare abundance, which we attribute to characteristics of the habitat classes. There appears a clear association between restored bog habitat and high mountain hare densities. Many studies of peatland restoration describe levels of degradation and potential effects of recovery interventions upon hydrology, water tables, soil quality, carbon and methane storage, and vegetation (Alderson et al., 2019;Bain et al., 2011;Holden et al., 2007;Page & Baird, 2016 Angerbjorn & Flux, 1995). Separately, snowshoe hare (L. americanus) densities reach up to 300 km −2 in boreal forests (Krebs et al., 2001).

| Degraded habitats
We observed wide variation of hare density between habitat types.
We found significant differences between habitat classes, which imply contrasts in vegetation diversity, forage quality, or attractiveness to hares. We detected a significant increase in density between 2017 and 18 followed by 2-3 years of decrease.
The Bleaklow surveys included 20 1-km 2 squares, which up to 2003 comprised eroded bare peat  or low levels of co-dominant heather (Anderson & Yalden, 1981). On those, Yalden (1971) recorded hares in only 8 1-km squares, and as single hare observations. By contrast, our surveys of 2017-21 in those same areas, now as restored bog, showed high densities of mountain hares, that is, 32.6 (95% CI: 25.2-42.2) hares km −2 ; in 2019 for Bleaklow overall 27.2 (95% CI 19.9-37.9) hares km −2 . This clearly suggests a positive impact of bog restoration on hare density. These restored areas have been shown to support higher floral diversity (Pilkington et al., 2016), which we suggest is attractive and beneficial to hares. Restoration, lime, and fertilizer applied to bare peat, potentially provided a lingering amount of phosphorous and nitrogen in the vegetation (Alderson et al., 2019), affording nutritional benefits to hares (Hewson, 1989;Miller, 1968;. Such might contribute to animal health and higher numbers . However, it is not clear whether food availability or nutritional quality limits hare populations (Keith, 1983;Newey et al., 2010) so it is hard to make inferences that food is the main cause of differences in hare density between habitats. It is also conceivable that where restoration elevated the water  (Anderson & Yalden, 1981). Density on grouse moor bog was significantly higher than unmanaged dwarf shrub heath. Density on grouse moor heather was also notably higher than unmanaged dwarf shrub heath, so the benefit to mountain hare density from heather burning and associated management activities described by Hesford et al. (2019) seemed apparent, as previously reported (Yalden, 1971). Yet, we observed the lower slopes of grouse moor heather were often dry, as also reported by Holden et al. (2015).
Frequent extensive heather burning reduced vegetation diversity and cover (Bonn et al., 2009, 178). On some of these areas, no hares were seen. On less frequently burned areas, groups of hares were occasionally observed feeding upon pioneer heather (Hewson, 1962(Hewson, , 1989. The grouse moor bog included deeper mature heather, where some hares hid, though finding movement difficult (Hewson, 1989;Stoddart & Hewson, 1984). Indeed, Yalden (1971) recorded fewer hares in areas of pure Calluna. We were unable to ascertain whether predator control on grouse moors was reducing levels of predation and contributing to higher densities of hares.
We estimated lower mountain hare densities on grouse moors than reported in Scotland (Hesford et al., 2019;Newey et al., 2003Newey et al., , 2018. In Scotland, high densities of mountain hares on grouse moors were first reported in four studies. Hewson (1965) reported game bags of 43-295 hares, annually 1955-63 on a 2 km 2 area.  produced raw count data estimating up to 300 hares km −2 . Stoddart and Hewson (1984) suggested an association of hares with grouse moors from game bags, estimating hares 42 km −2 .  reported count data, comparing density by habitat, with high densities in valleys 26.3 hares km −2 , on grouse moors in the Cairngorms 32.6 hares km −2 ; lower at arcticalpine areas 7.9 km −2 , suggesting grouse moor as optimum habitat.
More recently, studies in Scotland have shown the persistence of mountain hares measured in terms of occupied range and count indices as associated with moors managed for driven grouse shooting (Hesford et al., 2019(Hesford et al., , 2020. Very high densities (18-249 hares km −2 ) were recorded on grouse moors in northeast Scotland (Newey et al., 2018). In the Peak District, Yalden (1971Yalden ( , 1984 and Wheeler (2002) found highest counts on heather moorland, followed by bog and acid grassland.
It was, therefore, unexpected to find lower mountain hare density on grouse moors in the Peak District. Possibly mountain hares had shifted habitat use to high elevations, making for higher densities on the biologically diverse and higher altitude bogs. This could be a response to climate change and the rise in annual average temperatures observed in the Peak District (Caporn & Emmett, 2009, 47) and has been forecast across Europe (Leach et al., 2015). We speculate that Peak District heather moorland overlays acidic rock, which may contribute to lower forage quality and lower hare densities . itat class, disease, and parasites , contributing to similar dynamics. We reflect that in Scotland, grouse moor estates have conducted lethal removal of mountain hares (Patton et al., 2010). We then speculate whether the same occurred on grouse moors within the Peak District, causing lower and fluctuating mountain hare densities.
Mountain hare density on acid grassland showed high variation.
While containing much Nardus and Molinia disliked by mountain hares, some areas contained Calluna patches, enabling hares to feed, without trapping them within it. Unmanaged dwarf shrub heath areas mostly reported lowest hare densities. Its deep mature woody Calluna was frequently impenetrable. These findings are consistent with previous work by Yalden (1971), ), Hewson (1989. Acid grassland and unmanaged dwarf shrub areas were mostly at extent edges, possibly experiencing human pressure from higher road densities, walking paths, sheep farms, and settlements.

| Survey efficacy
The use of daylight distance sampling for mountain hares has been criticized as hares are nocturnal and rest up, hiding by day, resulting in lower observed encounter rates (Newey et al., 2018). However, our research achieved large sample sizes and encounter rates with narrow confidence intervals, a function of high densities on Bleaklow and Margery Hill, and demonstrating distance sampling by day can be effective. That said, we had deliberately chosen those areas for survey efficacy. By contrast, in mountain hare surveys on the Scottish Lammermuir hills, Pettigrew (2020)  We also considered differences in detection process between different habitat classes. Our surveys went on straight line transects, following the Jenkins et al. (1963) method of flushing hares from cover and were applied consistently to all habitat classes. Of note, the assessment of hare activity, that is, numbers of flushing hares, did not provide evidence that our surveys were missing hares hiding in deep heather. Indeed, all habitat classes contained winter vegetation up to ~100 cm height. Given that mountain hares can lie themselves down to ~15 cm height, they can hide in any habitat.
When assembling these analyses, we also considered several alternative habitat class definitions, for example, merging restored and unrestored bog; grouse moor bog and grouse moor heather.
Such alternatives did not change the substantive findings that bog habitats reported significantly higher density than managed grouse moor or acid grassland habitats. During surveys, when walking from one habitat to another, we typically observed an immediate abrupt change of encounter rates within <200 m.
We acknowledge that mountain hares may move between habitat classes and we did not employ telemetry to measure this. Hewson (1962Hewson ( , 1989 suggested hares would move by dusk to feed on grouse moor pioneer heather patches. We rarely observed such movement. Both the high elevation restored and unrestored bog areas contained some heather resource, obviating the need for a nightly migration. We analyzed habitat classes based on where each hare was first seen. We acknowledge field measurement factors may have contributed to small errors of habitat class allocation. Hare home ranges may be very small ~0.1 km 2 (Hewson & Hinge, 1990;Rao et al., 2003). Because our visual range exceeded 700 m and the study layout meant transects were 1000 m parallel to each other, we felt that coverage of home ranges was likely to be comprehensive.
Our surveys occurred without snow lie present, which might otherwise prompt hares to seek for heather which might better protrude out of the snow. Notwithstanding these challenges, our surveys achieved global detection probability of 18% of hares, that is, seeing nearly 1 in 5 hares to a range of 520 m. We duly consider distance sampling by day as effective across habitats.

| Population fluctuations
In the Peak District since 1971, there were four previous reports of mountain hare abundance suggesting a population of up to ~1000 individuals (Mallon, 2001). The distance sampling survey of winter 2001-2002 using different methods to this paper estimated abundance at ~12,000 hares (CI: 7000-20,000) (Mallon, 2001;Mallon et al., 2003;Wheeler, 2002). We retrieved that data and applied the same analyses as for 2017-21. This revised 2002 density estimate to 9.4 hares km −2 (95% CI 6.8 to 12.9); abundance for survey ex- Therefore, estimates for 2002 compared with 2019 appear similar and suggest a stable population. We speculate whether the increase in densities seen on restored bog has been balanced by a decrease in densities in other areas. Otherwise, the length of this study  is too short to detect population cycles, which are subject to complex factors .
Population dynamics for congeneric snowshoe hare suggest annual fluctuations with observed increases by 25%, or decreases by as much as 75%, linked to food supply and predation (Krebs et al., 2001). Cycle periodicity of mountain hares in Scotland has a range of 4-15 years, with amplitude of up to 90% , 8 years historically for Irish hare .
We cannot identify explicit causation for the population fluctuations we observed. Winter 2017-18 was exceptionally severe (UK Met Office, 2020), possibly causing additional mortality. Summer 2018 was extremely hot, potentially contributing to difficult breeding conditions arising from dry vegetation and reduced water availability. Under climate change, the range of mountain hares is forecast to move northwards and to higher elevations (Bedson, Devenish, et al., 2021;Leach et al., 2015;Rehnus et al., 2018), which may result in lower abundances.
This Peak District mountain hare population assessment shows how their confinement to the uplands, and sensitivity to different habitats, makes them a useful mammal species for ecosystem monitoring. They provide an understanding of mammalian responses to climate change: a cold-niche specialist at the periphery of their climatic range (Harris & Yalden, 2008). We suggest both degrading forces and restoration efforts impact upon hare density. There is substantial variation of density between habitat classes, predisposing the population to local extinction events (Patton et al., 2010). Management agendas should consider how future changes to habitat landcover and land use may affect this mountain hare population.

CO N FLI C T O F I NTE R E S T
None declared.  Note: n = number of observations; Model (key) = Key function with series expansion; AIC = Akaike information criterion; ΔAIC = delta AIC value within comparable data selections; χ 2 GOF (p) = chi-square goodness of fit p-value; P = detection probability function; P cv = detection probability coefficient of variation. We chose to use data truncated at 520 m with the hazard-rate model and polynomial, for all analyses.

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Note: S1 = Stratum 1; S2 = Stratum 2. D̂ difference subtracts S2 D̂ from S1 D̂. A positive value indicates Stratum 1 is larger; a negative value means Stratum 2 is larger. SE is the standard error of D̂ difference. Values are assessed with Satterthwaite t-test reporting t-statistic and degrees of freedom. Asterisk * and bold lines indicate p-value significant and using Bonferroni within-cohort correction.

TA B L E A 5
Pairwise t-tests comparing habitat class strata each year based on values from Note: Calculation of km 2 for each surveyed areas is based on relevant habitat classes only, that is, acid grassland; grouse moor bog; grouse moor heather; restored bog; unrestored bog; and unmanaged dwarf shrub heath. Thus non-relevant types, for example, woodland are excluded. Density estimate is shown with 95% confidence limits; abundance also with 95% confidence limits.

TA B L E A 6
Abundance of mountain hares for Peak District for year 2019, based on density estimates derived from pooled observations for each of the four denoted surveyed areas F I G U R E A 1 Encounter rate (hares km −1 ) by habitat class, by activity first observed for all Bleaklow and Margery Hill detections n = 1999. If groups, activity recorded as that of majority of hares. Histogram distance bin widths arranged at ~43 m increments as Figure 4. Note x-axis = radial distance observer to object, whereas Figure 4 x-axis represents perpendicular distance, hence differences between the two charts. When comparing summed encounters occurring either within or beyond 43 m for each habitat class, the highest proportion of activity was 56% of hares on unrestored bog beyond 43 m as stationary. Proportionately nearly twice as many observations on grouse moor bog or heather were of flushing hares, compared with restored or unrestored bog. Chart excludes records of 11 hare encounters where activity went unrecorded: 3 on restored bog and 8 on unrestored bog  Table A6